Animating the merging of multiple video strips
There are a couple ways, but I would use masks:




With a strip selected, add a mask modifier in the properties region (N) by pressing Add strip modifier > Mask. I also like to set the alpha blending to alpha over:



You can either use another strip to control the selected strip's alpha channel. You could use a scene strip to generate such a map based on the render output of a scene, or you could use an animated mask.
To create a mask, use the UV/image editor with the mode set to mask. Press &#8679; ShiftA and select the type of mask to create.
To animate it, transform it with G (translate) S (scale) and R (rotate). Insert keyframes with I.

To move the keyframes around/delete them, you can use the dopesheet in mask mode:




Unfortunately there doesn't seem to be any way to get the image editor to update in realtime at the moment, so you'll have to manually refresh it by pressing F12. For that to work, the viewed image must be set to Render result.

Result: